The comments drew swift and biting condemnation from his fellow candidates and some veterans groups, who called on Trump to apologize.

That's not how the business mogul and reality TV star sees it. He said he didn't refute the idea that McCain is a war hero (though he did say, "he's not a war hero" before modifying his remarks"), and that he was actually being critical of McCain's record on veterans issues.

"I'm very disappointed in John McCain because the vets are horribly treated in this country. I'm fighting for the vets. I've done a lot for the vets," Trump said. He said his fellow candidates were so quick to condemn him because he's been rising in the polls in recent weeks after generating yet another controversy after he called Mexican immigrants rapists and criminals.

Trump also argued that veterans who are not captured don't get sufficient attention.

"They get no credit. Nobody even talks about them. They're like forgotten," Trump said. "I think that's a shame, if you want to know the truth...Those are heroes also."

Trump also discussed his own deferments from the Vietnam War. He received both a student deferment and a minor medical deferment, which he said was for a minor bone spur on his foot. He was later entered into the lottery, but says he wasn't drafted because his number was too high.

"If I would have gotten a low number, I would have been drafted. I would have proudly served. But I got a number, I think it was 356. That's right at the very end," Trump said. "I was fortunate, in a sense, because I was not a believer in the Vietnam War. That was another war that was a disaster for this country."

Trump's explanations did little to quell the furor from his fellow Republicans on Sunday.

"I would recommend that he apologize and retract [his comments] and then get back to the campaign that he's been running on important issues like this Iran deal and the threat that it poses to the United States and the world," Sen. Tom Cotton, R-Arkansas and a veteran himself, said on NBC's "Meet the Press."

In a separate interview on the show, former Gov. Rick Perry, who is also running for the GOP nomination, doubled down on his call for Trump to apologize. Perry was one of the first Republicans to publicly condemn Trump for Saturday's comments.

"Until Mr. Trump apologizes directly to John McCain and also to the veterans of this country, I don't think he has the character or the temperament to hold the highest position in this country," Perry said.

Asked by host Chuck Todd whether Trump should be kicked out of the Republican debates, Perry said he would refer to the organizers. But, he added, "I'm real comfortable being on the stage with him and confronting him on a host of issues he's just wrong on."

Other 2016 contenders are growing increasingly derisive of Trump, especially in light of his recent comments regarding Mexican immigrants.

"We have to remember this is a man who spent his whole life saying outrageous things. So, early in his campaign, when he said something outrageous, people kind of said just ignore it and move on, it will go away. This is what he does for a living," Florida Sen. Marco Rubio said on CNN's "State of the Union." "I think now, as this has gone forward and he's become a more covered candidate and people pay more attention to him, it's required people to be more forceful on some of these offensive things that he's saying."